Collaborative Research: Stochastic Methods for Complex Systems

合作研究：复杂系统的随机方法

• 批准号: 1818726
• 负责人: David Aristoff
• 金额: $ 10万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-01 至 2021-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818726&HistoricalAwards=false
• 关键词: Collaborative; Research; Stochastic; Methods; Complex

This project addresses computational challenges in materials science, chemistry, uncertainty quantification, and related fields. Quantities of interest such as chemical reaction rates, strength of alloys, and more, can be estimated using a common mathematical modeling framework that computes mean values and provides quantification of the variance about the means. Estimating these quantities by computer simulation can be particularly challenging when the property that one wishes to study is rare and many repeated computer simulations would be required to estimate the mean value and the variance. While this challenge is somewhat alleviated by growth in computing power, some simulations, including chemical reaction rates, cannot be addressed via brute force computation. Rather than rely on raw computing power, the investigators intend to develop novel computer algorithms and approximations that will allow for more efficient and more accurate predictions. This includes the use of interacting copies of mathematical models, which communicate information between one another, resulting in higher quality estimates. These algorithms and approximations will allow more faithful prediction of quantities of interest and access to bigger models (such as larger, more complicated molecules). Mathematically the project will provide a rigorous understanding of the computer algorithms, providing confidence to scientists in a variety of fields. Multiscale distributions appear in a variety of applications, including materials science, chemistry, and uncertainty quantification. Given efficient sampling strategies, one can compute a variety of quantities of interest, including ensemble averages, mean first passage times, and probabilities of rare events. However, multiscale distributions in high number of dimensions are particularly challenging to sample. One example is the Boltzmann distribution induced by an energy landscape containing superbasins. Such a landscape features clusters of local minima that correspond to close groupings of modes in the distribution. This project will investigate four sampling algorithms: weighted ensemble sampling, parallel replica dynamics, local entropy smoothing, and piecewise deterministic Markov processes. Weighted ensemble sampling partitions state space into bins and then elects to sample within those bins in an optimal way. The project will investigate the choice of the sample allocation strategy and consider both finite and infinite system size limits for the method. Parallel replica dynamics also involves using an ensemble of samples, but, in contrast to weighted ensemble, it uses the replicas to efficiently find first exits out of one metastable region and into another. Local entropy smoothing removes the superbasin features of the energy landscape by performing local ensemble sampling and averaging. Finally, the investigators will use piecewise deterministic Markov processes to perform rejection free sampling without requiring estimates of gradients. These algorithms will be rigorously analyzed, and they will be tested on a variety of realistic high-dimensional problems including chemical reaction networks and stochastic molecular dynamics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目解决了材料科学，化学，不确定性量化和相关领域的计算挑战。 感兴趣的参数，如化学反应速率、合金强度等，可以使用通用的数学建模框架进行估计，该框架计算平均值并提供关于平均值的方差的量化。 当人们希望研究的属性很少并且需要多次重复的计算机模拟来估计平均值和方差时，通过计算机模拟估计这些量可能特别具有挑战性。 虽然计算能力的增长在一定程度上缓解了这一挑战，但一些模拟，包括化学反应速率，无法通过蛮力计算来解决。 研究人员打算开发新的计算机算法和近似值，而不是依赖原始的计算能力，以实现更有效、更准确的预测。 这包括使用相互作用的数学模型副本，这些模型彼此之间传递信息，从而产生更高质量的估计。 这些算法和近似将允许更忠实地预测感兴趣的量，并访问更大的模型（如更大，更复杂的分子）。 在数学上，该项目将提供对计算机算法的严格理解，为各个领域的科学家提供信心。 多尺度分布出现在各种应用中，包括材料科学，化学和不确定性量化。 给定有效的采样策略，可以计算各种感兴趣的量，包括系综平均值，平均首次通过时间和罕见事件的概率。 然而，在高维数的多尺度分布是特别具有挑战性的采样。 一个例子是由包含超级盆地的能量景观引起的玻尔兹曼分布。 这样的景观特征集群的本地最小值，对应于密切的模式组的分布。 本计画将探讨四种取样演算法：加权整体取样、平行复本动态、局部熵平滑及分段决定性马尔可夫过程。 加权集成采样将状态空间划分为仓，然后选择以最佳方式在这些仓内进行采样。 该项目将研究样本分配策略的选择，并考虑有限和无限系统大小限制的方法。 并行副本动力学也涉及使用样本的集合，但是，与加权集合相反，它使用副本来有效地找到一个亚稳态区域的第一个出口并进入另一个亚稳态区域。 局部熵平滑通过执行局部集合采样和平均来去除能量景观的超盆地特征。 最后，研究人员将使用分段确定性马尔可夫过程来执行无拒绝抽样，而无需估计梯度。 这些算法将被严格分析，并将在各种现实的高维问题上进行测试，包括化学反应网络和随机分子动力学。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Transient probability currents provide upper and lower bounds on non-equilibrium steady-state currents in the Smoluchowski picture

• DOI: 10.1063/1.5120511
• 发表时间: 2019-11-07
• 期刊: JOURNAL OF CHEMICAL PHYSICS
• 影响因子: 4.4
• 作者: Copperman, Jeremy;Aristoff, David;Zuckerman, Daniel M.
• 通讯作者: Zuckerman, Daniel M.

Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs

推广并行副本动力学：轨迹片段、异步计算和 PDMP

• DOI: 10.1137/18m1177792
• 发表时间: 2019
• 期刊: SIAM/ASA Journal on Uncertainty Quantification
• 作者: Aristoff, David